Solve the system of equations. $\begin{aligned} &3x+4y = -23 \\\\ & x=3y+1 \end{aligned}$ $ x=$
Answer: We are given that ${x}={3y+1}$. Let's substitute this expression into the first equation and solve for $y$ as follows: $\begin{aligned} 3{x}+4y &= -23\\\\ 3\cdot({3y+1})+4y&=-23\\\\ 9y+3+4y&=-23\\\\ 13y&=-26\\\\ y&=-2 \end{aligned}$ Since we now know that ${y}={-2}$, we can substitute this value in the second equation to solve for $x$ as follows: $ \begin{aligned} x &= 3\cdot{y}+1 \\\\ x&=3\cdot({-2})+1\\\\ x&=-5 \end{aligned}$ This is the solution of the system: $\begin{aligned} &x = -5 \\\\ &y=-2 \end{aligned}$